I figured why not collate our anecdotal data. You can find Critical Encounter or FATE data for OC in your achievements under Field Operations. Non-OC FATEs have an achievement but that may be hard to decipher from the ones you've done prior to OC.
My CE and FATE tallies are separate. Division shows they are 20% and 5% respectively (edit: SE confirmed CEs are 20% and FATEs are 5%), but linear regression shows they are 25-30% and 10% respectively so far:
CE Data:
19.78% (37 Atma / 187 CEs * 100)
FATE Data:
4.85% (18 Atma / 371 FATEs * 100)
6.84% (5 Atma / 73 FATEs * 100)
Mixed Data:
4.37% (7 Atma / (57 CEs + 103 FATEs) * 100)
7.63% (20 Atma / (97 CEs + 165 FATEs) * 100)
8.33% (6 Atma / (32 CEs + 40 FATEs) * 100)
8.62% (22 Atma / (93 CEs + 162 FATEs) * 100)
10% (2 Atma / (10 CEs + 10 FATEs) * 100)
12.98% (20 Atma / (74 CEs + 80 FATEs) * 100)
13.08% (14 Atma / (56 CEs + 51 FATEs) * 100)
13.26% (13 Atma / (48 CEs + 50 FATEs) * 100)
25% (7 Atma / (12 CEs + 16 FATEs) * 100)
You can certainly see that the average for most seems to be 7-13% when both are included. I'm going to keep updating my CE and FATE specific data as I level all my Phantom jobs, but so far it looks rather substantial of a difference.